// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_DETERMINANT_H
#define EIGEN_DETERMINANT_H

namespace Eigen {

namespace internal {

template<typename Derived>
EIGEN_DEVICE_FUNC inline const typename Derived::Scalar
bruteforce_det3_helper(const MatrixBase<Derived>& matrix, int a, int b, int c)
{
	return matrix.coeff(0, a) * (matrix.coeff(1, b) * matrix.coeff(2, c) - matrix.coeff(1, c) * matrix.coeff(2, b));
}

template<typename Derived, int DeterminantType = Derived::RowsAtCompileTime>
struct determinant_impl
{
	static inline typename traits<Derived>::Scalar run(const Derived& m)
	{
		if (Derived::ColsAtCompileTime == Dynamic && m.rows() == 0)
			return typename traits<Derived>::Scalar(1);
		return m.partialPivLu().determinant();
	}
};

template<typename Derived>
struct determinant_impl<Derived, 1>
{
	static inline EIGEN_DEVICE_FUNC typename traits<Derived>::Scalar run(const Derived& m) { return m.coeff(0, 0); }
};

template<typename Derived>
struct determinant_impl<Derived, 2>
{
	static inline EIGEN_DEVICE_FUNC typename traits<Derived>::Scalar run(const Derived& m)
	{
		return m.coeff(0, 0) * m.coeff(1, 1) - m.coeff(1, 0) * m.coeff(0, 1);
	}
};

template<typename Derived>
struct determinant_impl<Derived, 3>
{
	static inline EIGEN_DEVICE_FUNC typename traits<Derived>::Scalar run(const Derived& m)
	{
		return bruteforce_det3_helper(m, 0, 1, 2) - bruteforce_det3_helper(m, 1, 0, 2) +
			   bruteforce_det3_helper(m, 2, 0, 1);
	}
};

template<typename Derived>
struct determinant_impl<Derived, 4>
{
	typedef typename traits<Derived>::Scalar Scalar;
	static EIGEN_DEVICE_FUNC Scalar run(const Derived& m)
	{
		Scalar d2_01 = det2(m, 0, 1);
		Scalar d2_02 = det2(m, 0, 2);
		Scalar d2_03 = det2(m, 0, 3);
		Scalar d2_12 = det2(m, 1, 2);
		Scalar d2_13 = det2(m, 1, 3);
		Scalar d2_23 = det2(m, 2, 3);
		Scalar d3_0 = det3(m, 1, d2_23, 2, d2_13, 3, d2_12);
		Scalar d3_1 = det3(m, 0, d2_23, 2, d2_03, 3, d2_02);
		Scalar d3_2 = det3(m, 0, d2_13, 1, d2_03, 3, d2_01);
		Scalar d3_3 = det3(m, 0, d2_12, 1, d2_02, 2, d2_01);
		return internal::pmadd(-m(0, 3), d3_0, m(1, 3) * d3_1) + internal::pmadd(-m(2, 3), d3_2, m(3, 3) * d3_3);
	}

  protected:
	static EIGEN_DEVICE_FUNC Scalar det2(const Derived& m, Index i0, Index i1)
	{
		return m(i0, 0) * m(i1, 1) - m(i1, 0) * m(i0, 1);
	}

	static EIGEN_DEVICE_FUNC Scalar
	det3(const Derived& m, Index i0, const Scalar& d0, Index i1, const Scalar& d1, Index i2, const Scalar& d2)
	{
		return internal::pmadd(m(i0, 2), d0, internal::pmadd(-m(i1, 2), d1, m(i2, 2) * d2));
	}
};

} // end namespace internal

/** \lu_module
 *
 * \returns the determinant of this matrix
 */
template<typename Derived>
EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar
MatrixBase<Derived>::determinant() const
{
	eigen_assert(rows() == cols());
	typedef typename internal::nested_eval<Derived, Base::RowsAtCompileTime>::type Nested;
	return internal::determinant_impl<typename internal::remove_all<Nested>::type>::run(derived());
}

} // end namespace Eigen

#endif // EIGEN_DETERMINANT_H
